Macc might have taken the lead as early as the second minute when veteran striker Simon Yeo out-muscled David Buchanan, only to scuff his drive inches wide of the far post from 15 yards.
However just two minutes later Yeo flicked a header onto the crossbar for strike partner Martin Gritton to head home from close range.
The joy was short-lived as Bury scored before the cheers had died down, with Andy Bishop releasing Stephen Dawson who completed a surging run with a thumping drive from 15 yards.
Macc might have re-taken the lead on seven minutes when Nathan Brown saw his rising shot from the edge of the box well saved by his namesake Wayne Brown.
Bury striker Bishop had two chances for the Shakers before the break, firing one badly over the bar and seeing another shot on the turn well saved by Jonny Brain.
But Town were unlucky not to go ahead on the stroke of half-time when a deflected drive from Terry Dunfield was superbly palmed wide by Brown.
The best chance of the second half came moments after the break when Yeo broke loose only for Brown to produce a stunning low stop.
Macclesfield had appeals for a penalty waived away when Dawson got man and ball with a challenge on Dunfield, before Macc were reduced to ten men when Matthew Flynn was sent off for a second bookable offence.
However Bury could not capitalise, barely managing to muster a single chance, with only sub Andy Morrell looking dangerous with a clever chip that was finger-tipped over the bar by Brain.